Homogenization of elastic materials containing self-similar microcracks
Mustapha El Jarroudi, Mustapha Er‐Riani · The Quarterly Journal of Mechanics and Applied Mathematics · 2018
We consider elastic materials containing microcracks located along Sierpinski carpet fractals. We suppose that the microcracks are rectilinear in the two-dimensional case and small surfaces in the three-dimensional case. We use |$\Gamma$|-convergence methods in order to study the asymptotic behavior of the structures with respect to vanishing parameters describing the thickness of small-scale barriers separating the microcracks. We derive the effective boundary conditions on the Sierpinski carpet interfaces.